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The OpenTripPlanner multimodal journey planning system
There is a newer version: 2.6.0
package org.opentripplanner.routing.util.elevation;

/**
 * 
 * Tobler's hiking function is an exponential function determining the hiking speed, taking into
 * account the slope angle. It was formulated by Waldo Tobler. This function was estimated from
 * empirical data of Eduard Imhof. [ Wikipedia
 * ]
 * 
 *  * Walking speed(W):
 *
 *     W = 6 m/s * Exp(-3.5 * Abs(dh/dx + 0.05))
 * 
 *
 * 
 * The {@code 6 m/s} is the Maximum speed achieved. This happens at angle 2.86 degrees or -5%
 * downhill. In OTP we want to apply this as a multiplier to the horizontal walking distance. This
 * is done for all walkable edges in the graph. To find the walkingtime for an edge we use the
 * horizontal walking speed. Therefore:
 * 
 *  * Given:
 *   Vflat : Speed at 0 degrees - flat
 *   Vmax  : Maximum speed (6 m/s)
 *
 *   Vmax = C * Vflat
 *
 * Then:
 *               1
 *   C = ------------------  = 1.19
 *        EXP(-3.5 * 0.05)
 * And:
 *
 *   dx = Vflat *  t
 *   W = C * Vflat * EXP(-3.5 * ABS(dh/dx + 0.05))
 *
 * The Horizontal walking distance multiplier(F) then becomes:
 *
 *                      1
 *   F = -----------------------------------
 *        C * EXP(-3.5 * ABS(dh/dx + 0.05))
 *
 * Examples:
 *
 *   Angle  | Slope % | Horizontal walking distance multiplier
 *   -------+---------------------------------------
 *    19,3  |   35 %  |  3,41
 *    16,7  |   30 %  |  2,86
 *    14,0  |   25 %  |  2,40
 *    11,3  |   20 %  |  2,02
 *     8,5  |   15 %  |  1,69
 *     5,7  |   10 %  |  1,42
 *     2,9  |    5 %  |  1,19
 *     0,0  |    0 %  |  1,00
 *    −2,9  |   −5 %  |  0,84
 *    −5,7  |  −10 %  |  1,00
 *    −8,5  |  −15 %  |  1,19
 *   −11,3  |  −20 %  |  1,42
 *   −14,0  |  −25 %  |  1,69
 *   −16,7  |  −30 %  |  2,02
 *   −19,3  |  −35 %  |  2,40
 *   −21,8  |  −40 %  |  2,86
 *   −24,2  |  −45 %  |  3,41
 * 
 */
public class ToblersHikingFunction {

  /**
   * The exponential growth factor in Tobler´s function.
   */
  private static final double E = -3.5;

  /**
   * The slope offset where the maximum speed will occur. The value 0.05 will result in a maximum
   * speed at -2.86 degrees (5% downhill).
   */
  private static final double A = 0.05;

  /** The horizontal speed to maximum speed factor: Vmax = C * Vflat */
  private static final double C = 1 / Math.exp(E * A);

  private final double walkDistMultiplierMaxLimit;

  /**
   * @param walkDistMultiplierMaxLimit this property is used to set a maximum limit for the
   *                                   horizontal walking distance multiplier. Must be less than
   *                                   1.0. See the table in the class documentation for finding
   *                                   reasonable values for this constant.
   */
  public ToblersHikingFunction(double walkDistMultiplierMaxLimit) {
    if (walkDistMultiplierMaxLimit < 1.0) {
      throw new IllegalArgumentException(
        "The 'walkDistMultiplierMaxLimit' is " +
        walkDistMultiplierMaxLimit +
        ", but must be greater then 1."
      );
    }
    this.walkDistMultiplierMaxLimit = walkDistMultiplierMaxLimit;
  }

  /**
   * Calculate a walking distance multiplier to account tor the slope penalty.
   *
   * @param dx The horizontal walking distance
   * @param dh The vertical distance (height)
   */
  public double calculateHorizontalWalkingDistanceMultiplier(double dx, double dh) {
    double distanceMultiplier = 1.0 / (C * Math.exp(E * Math.abs(dh / dx + A)));

    return distanceMultiplier < walkDistMultiplierMaxLimit
      ? distanceMultiplier
      : walkDistMultiplierMaxLimit;
  }
}